Let's be very reductionist and say that the prevalence of crime is affected by people's biology, their upbringings, social environment and finally the crime and punishment system. In many ways the hardest things to change are their biology, so let's just ignore these for the time being (although see 12).
Then what we have are upbringings/society and the crime and punishment system. Being very broad brushed we could say that before 1800 people put little faith in the former and lots in the latter. Nowadays people tend to be split between whether they place their faith in being tough on crime or tough on the causes of crime (can't resist dropping this link here).

I favour both approaches, but outside of the fact that being just selected into a better school makes you a bit less likely to commit crimes, most social interventions we know don't seem to have much effect. It might be a dead end. Start with the fact that 65% of UK boys with a father in prison will go on to offend. That's easy to understand on the social-upbringing account: these people probably lack nurturing environments, live in bad neighbourhoods and so on.

The problem is that these just-so explanations don't seem to fit the data.

Parenting: here's a 2015 US paper showing "very little evidence of parental socialization effects on criminal behavior before controlling for genetic confounding and no evidence of parental socialization effects on criminal involvement after controlling for genetic confounding".

Family income: here's a 2014 Swedish paper showing "here were no associations between childhood family income and subsequent violent criminality and substance misuse once we had adjusted for unobserved familial risk factors".

Bad neighbourhood: here's a 2013 Swedish paper finding "the adverse effect of neighbourhood deprivation on adolescent violent criminality and substance misuse in Sweden was not consistent with a causal inference. Instead, our findings highlight the need to control for familial confounding in multilevel studies of criminality and substance misuse". (In fact, this weird 2015 US paper found that low-income boys surrounded by affluent neighbours committed more crimes).

I realise there are other studies saying different things—I don't want to sci-jack or be the Man of One Study—but many of these use caveman methodologies that don't even attempt to account for the potential that some people are born different to others (e.g. some have more testosterone). And I think we can be cautiously confident in these findings because they fit with other things we know.

So we're left with enforcement. Can that make a difference? Today black Americans commit many more crimes per capita than whites, despite committing fewer than them in the late 19th Century. It's possible that the results above are only true for a narrow range of environments, and thus that social-familial affects are driving this.

But in any case do we really think that blacks in today's USA live in worse environments than the blacks of the post-bellum USA? If environments are improving and people are pretty much the same genetically, then the criminal justice system may be the big changing factor.

Some way of changing improper or inadequate enforcement—e.g. liberalising drug laws—may be a can opener to assume but it's nothing like the assuming the can opener of changing genetics or magic social interventions that actually work.